Tractable nonlinear capacity models for aggregate production planning

A fundamental problem in developing aggregate planning models for production has been their inability to accurately reflect the nonlinear dependency between workload and lead times. This typically leads to significant disparity between planned and actual lead times since capacity and lead time are highly dependent on product mix and workload. We capture the relationship between capacity and workload at an aggregate level with nonlinear Clearing Functions that allow us to embed them in a mathematical programming model. A partitioning scheme is introduced to divide capacity across products, addressing the effects of varying product mix. A comprehensive computational experiment illustrates the benefits of this approach in comparison to conventional fixed capacity and fixed lead time approaches.